1. Personal Finance

2. Definitions
There are many definitions that need to be known in this unit.
Term: The length of an investment or loan
Principle: the amount of money you borrow. It is usually the difference between the selling price and your down payment for a loan.
Interest: the amount of money earned on an investment or paid on a loan above and beyond the principle amount.
Maturity: the end date of an investment or loan at the end of the term.
Future Value: The amount that an investment will be worth after a specified period of time.

3. Compound Periods: Corresponds to the number of payments you will make or the number of times the interest will be added. Annual is once a year, semi-annual is twice, quarterly is 4 times, monthly is 12 times, semi-monthly is 24 times and bi-weekly is 26 times a year.
Simple Interest: is the amount of interest earned or paid based on the principle and the simple interest rate. In other words, the amount of interest will be the same every year of the loan or investment.
Compound Interest; the interest that is earned or paid on both the principle and the accumulated interest. Here, the amount of interest will be different every year/term.
Rule of 72: a formula that estimates the doubling time of an investment. It is 72/I%. Works best with annual compounds.

4. Simple Interest
As defined earlier, simple interest applies the interest rate only to the principle amount.
The formula is:
i = prt where i = interest earned
p = principle
r = interest rate in decimal
t = time in years
ex: Mary invested $2500 in a guaranteed investment certificate (GIC) at 2.5% simple interest, paid annually, with a term of 10 years. How much interest will she earn and what is her future value?
i = prt
= (2500)(0.025)(10)
= $625
Future Value = principle + interest =
= $3125

5. ex 2: Grant invested $20,000 in a simple interest Canadian Savings Bond (CSB) that paid annual interest. a) If the future value is $29,375 at the end of 5 years, what was the interest rate? i = – = 9375 i = prt 9375 = (20000)(r)(5) (20000)(5) (20000)(5) r = = 9.38% b) Grant cashed in after 4.5 years. How much money did he end up with using the same info? i = (20000)(0.0938)(4) i = $ = $27,504
Only put 4 as time because we have to deal in full years!
Add back in the principle when looking for a total amount.

6. A = P + Prt where A is the future value
Sometimes we are given the future value (ie, not given the interest earned) without the principle so we need a modified formula to solve these problems:
A = P + Prt where A is the future value
P is the principle
r is the rate (decimal)
t is the time (years)
ex: An investment company is offering a simple interest rate of 4.3% for a GIC with a 6 year term. What principle would you need to invest if you want to have $15 000?
A = P + Prt can also look like A = P(1+rt)
15000 = P(1 + (0.043)(6))
15000 = P(1.258)
P = $

7. Some questions may ask for the rate of return on an investment.
All rates are percentages written in decimal form
You will need the following formula:
Rate of Return = interest earned x 100
principle
ex: What is the rate of return of a $ investment that had the future value of $30 500?
Interest Earned = –
= $5500
Rate of Return = x 100
25000
= 22%

8. Compound INterest
For compound interest, we use your calculator so you can calculate your payments, future values and present/principle values.
On your TVM solver (Either 2nd Finance or Apps 1)
N = Number of payment periods (amortization x payment plan)
I% = interest rate
PV = present value (principle amount)
PMT = payment amount (positive or negative)
FV = future value (will be negative)
P/Y = payments per year
C/Y = compounds per year
To solve, put your cursor in the desired spot and press ALPHA ENTER.

9. Don’t forget the rule of 72:
You need to know that PMT is positive when investing in yourself but negative when paying a fee to someone
Don’t forget the rule of 72:
Doubling Time = 72 %
ex: Berta and Kris invested $5000 in a CSB. Berta’s earns 8% compounded annually, while Kris’s earns 9% compounded annually. Estimate the doubling time for both investments.
Berta = 72/8
= 9 years
Kris = 72/9
= 8 years

10. $449.90 was earned in interest!
ex 2: Darva wants to go to Australia in 5 years to work. She needs to save up airfare so she saves up $500 every 6 months and puts it into a money market account. The account earns 3.8% compounded semi-annually. How much money will she have earned in 5 years?
5 years * 2 P/Y = 10
She has earned $
She saved $500 * 10 = $5000 so,
$ $5000 =
$ was earned in interest!

11. Interest Calculations

12. a) How much money should they invest?
ex: Agnes and Bill want to set up a music studio. They need $40,000 and to get it, they plan to set up the studio in 3 years and the bank will give them a loan at 9.6%, compounded quarterly, to save for it.
a) How much money should they invest?
b) How much interest will they earn over the term of their investment?
3 years * 4 P/Y = 12
They need to invest $30,
All FV’s should be negative
They will earn $ in interest

13. b) How much interest will she earn over the 20 years?
ex 2: Celia wants to have $300,000 in 20 years to retire. Celia has found an account that earns 10.8%, compounded annually.
a) What regular payments must Celia make at the end of each year to meet her $300,000 goal?
b) How much interest will she earn over the 20 years?
20 years * 1 P/Y = 20
She must make annual payments of $
Celia will earn $204, in interest over the 20 years!

14. Some questions will ask you for the number of payments or a number of years.
Don’t forget to take into account the number of times a year the payments will be made before you report your final answer.
ex: On Luis’ 20th birthday he started putting $1000 into a savings account every 6 months. The savings account has a rate of 3.5%, compounded semi-annually. At what age will he have more than $18000?
15.78 payments = 16 payments
BUT, there are 2 payments per year so the 16 payments is 8 years!
Luis will be 28 years old when he has $18,000.

15. LOANS
When you borrow money, you must repay the loan in a set period of time and with a certain amount of interest.
Don’t forget that when you are using your TVM the PMT values will be negative for loans because you are paying someone else the money.
When you are reporting your answers, you must never report a negative answer. If the PMT is negative, you say it is money being paid. If the FV is negative that means that you have that much money left (ie, your account is not overdrawn)

16. ex: Trina borrowed $10,000 at a rate of 6% compounded annually to pay for school. The loan is to be repaid in a single payment on the maturity date at the end of 5 years. How much will Trina need to pay back?
She will have to pay back $13, of which $ is the accumulated interest

17. a) How much can she borrow?
ex 2: Annette wants to redo her kitchen so her bank will charge her 3.6%, compounded quarterly. She already has a 10 year GIC that will mature in 5 years. When her GIC reaches maturity, Annette wants to use the money to repay the loan with one payment. She wants the amount of the payment to be no more than $20,000.
a) How much can she borrow?
b) How much interest will she pay?
5 years (maturity of GIC) * 4 P/Y = 20
**The 10 years for the GIC is IRRELEVANT!**
She can borrow a maximum of
$16,
She will pay $ in interest

18. ex 3: You have $25, to invest. There are two options: a)5% compounded annually b) 7% compounded annually with a $400 management fee. Which option is better after 10 years?
10 years x 1 payment/year
$400 management fee
Option b is better by $
$43, $40,722.37

19. Mortgages
Mortgages are loans made for the purchase of real estate in which the land is used to secure the loan.
For mortgage calculations, we will use our TVM solver exactly like we did for loans. The only difference is that the C/Y is always 2 unless otherwise stated.
You must watch your calculator because as soon as you change your P/Y, the C/Y will also change!

20. ex: What would be the monthly mortgage payment if you had a $50,000 mortgage at 8% for a 15 year amortization period? How much would you pay in total at the end of the 15 years? N = 15 x 12
= 180
amortization
payment #
$ per month
For the 15 years:
$ x 180 months
= $85,334.40

21. ex: You buy a condo for $100,000. 00 with a down payment of $20,000
ex: You buy a condo for $100, with a down payment of $20, at 6.5% compounded monthly for an amortization period of 25 years. How much interest have you paid after the first 10 years?
25 x 12
$ per month
“compounded monthly”
12 payments x 10 years
$46, in interest after 10 years

22. Principle calculations

23. ex: How much principle have you paid towards your $80,000
ex: How much principle have you paid towards your $80, mortgage at 6.5% compounded monthly for a 25 year amortization period after 15 years?
12 monthly payments x 15 years
$32, has been paid towards the original $80,000.
That means you still have to pay $47, back to the mortgage lender.

24. Credit Cards
There are many different forms of credit cards that can be obtained through a variety of sources.
Many have very high interest rates, usually between 15 – 25%.
While credit cards can get a person into trouble easily, they can also be a benefit for your credit score so long as you keep paying them off each month.
To calculate these problems, we use the TVM just like for loans.

25. ex: You are buying furniture worth $1075 on credit
ex: You are buying furniture worth $1075 on credit. You can make $75 payments and have two options. Which would you choose? Option A: The furniture store credit card which is offering a $100 rebate off the purchase price and an interest rate of 18.7% compounded daily. Option B: A new bank credit card, which has an interest rate of 15.4%, compounded daily, but no interest for the first year. Option A 1075 – 100 = 975 = PV
First figure out how long it will take to pay off then use the interest function to figure out how much on top of the initial amount you paid in TOTAL.!
It will take 15 payments
Total Paid:
= $

26. You should use the bank credit card as it has a lower total cost!
Option B 12 payments of $75 interest free = $900 So, 1075 – 900 = 175 = PV
She must make 3 payments
Total Paid: $
= $
You should use the bank credit
card as it has a lower total cost!

27. Appreciation vs. Depreciation
Appreciation is an increase in the value of an asset over time, usually expressed as a percentage.
When dealing with items that appreciate, we always take 1 + % (ie, if something appreciates at 5% then the rate is 1.05)
Depreciation is a decrease in the value of an asset over time, usually expressed as a percentage.
When dealing with assets that depreciate, we take 1 - % (ie, if something depreciates at a rate of 11% then the rate is 0.89)

28. ex: Lance wants to have a home office
ex: Lance wants to have a home office. He has two options: i) he could sign a 3 year lease with monthly rental payments of $2000. ii) he could buy a $ house with a 5% down payment. The bank would give him a 15 year mortgage at 5%, compounded semi-annually, paid monthly. Assume appreciation of 2% yearly. a) What are the costs of leasing over 15 years? 2000 * 15 * 12 = $360,000
cost
montly payments
years

29. b) What are the costs of buying over 15 years. 285,000
b) What are the costs of buying over 15 years? 285,000 * .95 = $270,750 = PV
5% down payment = 1 – 0.05 = 0.95
15 years * 12 P/Y
Buying Cost = Down payment + (number of payments)(cost)
= ( )
= $398,342.10
Value of House = initial value * Appreciation value
= 285,000(1.02)15
= $383,572.48
Actual Cost = buying cost – home value
= 398, – 383,572.48
= $14,769.62